Anything thrown, hurled, tossed, pitched, or otherwise flung into the air follows a path coinciding with the graph of a quadratic function.
Other phenomena behave in a quadratic fashions as well. The main cables of a suspension bridge follow the graph of a quadratic function.
A TV dish has a quadratic shape. Quadratic functions are everywhere.
The graph of a quadratic function is a parabola. This simulation will let you experiment with quadratic functions and parabolas.
A quadratic function is usually written in one of two different forms, the standard form and the expanded form. Choose the form you wish to experiment with. You can change to the other form at any time.
Next, enter the coefficients of the form you chose. Use the sliders or enter the numbers directly into the entry fields.
For the standard form, enter the leading coefficient a, and the x- and y- value of the vertex, h and k.
For the expanded form, enter the value of the leading coefficient a, the linear coefficient b, and the constant c.
You can see how the values you enter are related to the shape of the graph, and by changing forms, you can see how they are related to the values in the other form.
Experiment and try to determine how changing one of the values affects the graph and the other values. Some of the effects are easier to figure out than others. Good luck!